I am looking to use R as a MATLAB replacement for linear algebra.
I've done a fairly good job for finding replacements for most of the
functions I'm interested in, I
John Fox wrote a program for implementing the reduced row echelon form
of a matrix (by doing the Gauss-Jordan elimination). I modified it a
bit:

I wrote a program for implementing row echelon form, which is only
concerned with the getting the lower triangular part to be zero, along
with the first non-zero entry in each non-zero row being a one. Here
is what I wrote: